Work, Energy and Power

A body is projected vertically upwards with a velocity of $20 \mathrm{~ms}^{-1}$. If the potential energy of the body at a height of 5 m from the ground is 100 J , then the kinetic energy of the body at a height of 10 m from the ground is
(...

If a force $(\beta \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body displaces it through $(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+1 \hat{\mathbf{k}}) \mathrm{m}$, then the work done by the force on the bod...

If a position dependent force $\left(3 x^2-2 x+7\right) \mathrm{N}$ acting on a body of mass 2 kg displaces it from $x=0 \mathrm{~m}$ to $x=5 \mathrm{~m}$, then the work done by the force is

If the potential energy of a particle of mass 0.1 kg moving along $X$-axis is $5 x(x-4) \mathrm{J}$, then the speed of the particle is maximum at a position of

A motor can pump 7560 kg of water per hour from a well of depth 100 m . If the efficiency of the pump is $70 \%$, then power of the pump is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

If a constant force of $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}) \mathrm{N}$ acting on a body of mass 5 kg displaces it from $(3 \hat{\mathbf{i}}-4 \hat{\mathbf{k}}) \mathrm{m}$ to $(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3...

If a force $\mathbf{F}=(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}) \mathrm{N}$ acting on a body displaces it from point $(1 \mathrm{~m}, 2 \mathrm{~m})$ to point $(2 \mathrm{~m}, 0 \mathrm{~m})$, then work done by the force is

A body of mass ' $M$ ' is moving with a uniform speed of ' $V^{\prime}$ on a frictionless horizontal surface under the influence of two forces $F_1$ and $F_2$ as shown in the figure. The net power of the system is

A car of mass 2000 kg is accelerating from rest. If its engine is supplying constant power of 10 kW , then the velocity of the car at a time of 10 s is

If a force of $\left(6 x^2-4 x\right) \mathrm{N}$ acts on a body of mass 10 kg , then work to be done by the force in displacing the body from $x=2 \mathrm{~m}$ to $x=4 \mathrm{~m}$ is

A circular well of diameter 2 m has water upto the ground level. If the bottom of the well is at a depth of 14 m , the time taken in seconds to empty the well using a 1.4 kW motor is
(Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A body is projected at an angle of $60^{\circ}$ with the horizontal. If the initial kinetic energy of the body is $X$, then its kinetic energy at the highest point is

A body is moving along a straight line under the influence of a constant power source. If the relation between the displacement $(s)$ of the body and time $(t)$ is $s \propto t^x$, then $x=$

A train of mass $10^6 \mathrm{~kg}$ is moving at a constant speed of $108 \mathrm{~km} / \mathrm{h}$. If the frictional force acting on it is 0.5 N per 100 kg , then the power of the train is

A crane of efficiency $80 \%$ is used to lift 8000 kg of coal from a mine of depth 108 m . If the time taken by the crane to lift the coal is one hour, then the power of the crane (in kW ) is
(Acceleration due to gravity $=10 \mathrm{~ms}^{...

Two bodies $A$ and $B$ of masses 20 kg and 5 kg respectively are at rest. Due to the action of a force of 40 N separately, if the two bodies acquire equal kinetic energies in times $t_A$ and $t_B$ respectively, then $t_A: t_B=$

The bob of a simple pendulum of length 200 cm is released from horizontal position. If $10 \%$ of its initial energy is lost due to air resistance, then the speed of bob at the mean position is
(Acceleration due to gravity $=10 \mathrm{~ms}...

A person holds a ball of mass 0.25 kg in his hand and throws it, so that it leaves his hand with a speed of $12 \mathrm{~ms}^{-1}$. In this process, if his hand moved through a distance of 0.9 m , then the net force acted on the ball is

The power required for an engine to maintain a constant speed of $50 \mathrm{~ms}^{-1}$ for a train of mass $3 \times 10^6 \mathrm{~kg}$ on rough rails is
(The coefficient of kinetic friction between the rails and wheels of the train is 0.0...

The linear momentum of a body of mass 8 kg is $24 \mathrm{~kg} \mathrm{~ms}^{-1}$. If a constant force of 24 N acts on the body in the direction of motion of the body for a time of 3 s , then the increase in the kinetic energy of the body i...

A particle of mass $m$ at rest on a rough horizontal surface with a coefficient of friction $\mu$ is given a
velocity $u$. The average power imparted by friction before it stops

The average power generated by a 90 kg mountain climber who climbs a summit of height 600 m in 90 min is (Acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

A body thrown vertically upwards from the ground reaches a maximum height $H$. The ratio of the velocities of the body at heights $\frac{3 H}{4}$ and $\frac{8 H}{9}$ from the ground is

A force of $(4 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}) \mathrm{N}$ is action on a particle of mass 2 kg displaces the particle from a position of $(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})$ $m$ to a position of ...

A spring of spring constant $200 \mathrm{~N}-\mathrm{m}^{-1}$ is initially stretched by 10 cm from the unstretched position. The work to be done to stretch the spring further by another 10 cm is

The upper $\left(\frac{1}{n}\right)$ th of an inclined plane is smooth and the remaining lower part is rough with coefficient of friction $\mu_k$. If a body starting from rest at the top of the inclined plane will again come to rest at the...

A light body of momentum $p_L$ and a heavy body of momentum $p_H$ both have the same kinetic energy, then

A machine with efficiency $\frac{2}{3}$ used 12 J of energy in lifting 2 kg block through certain height and it is allowed to fall through the same. The velocity while it reach the ground is

A $4 \mathrm{~kg}$ mass is suspended as shown in figure. All pulleys are frictionless and spring constant $k$ is $8 \times 10^3 \mathrm{Nm}^{-1}$. The extension in spring is $\left(g=10 \mathrm{~ms}^{-2}\right)$

Two bodies $A$ and $B$ of masses $2 m$ and $m$ are projected vertically upwards from the ground with velocities $u$ and $2 u$ respectively. The ratio of the kinetic energy of body $A$ and the potential energy of body $B$ at height equal to ...

A force of $\left(6 x^2-4 x+3\right) \mathrm{N}$ acts on a body of mass 0.75 kg and displaces it from $x=2 \mathrm{~m}$ to $x=5 \mathrm{~m}$. The work done by the force is

A spring of $5 \times 10^3 \mathrm{Nm}^{-1}$ spring constant is stretched initially by 10 cm from unstretched position. The work required to stretch it further by another 10 cm is

A machine gun fires 300 bullets per minute each with a velocity of $500 \mathrm{~ms}^{-1}$. If the mass of each bullet is 4 g . The power of the machine gun is

In the case of non-conservative forces, the following statement is correct.

A body of mass 2 kg is moving with a constant acceleration of $(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}) \mathrm{ms}^{-2}$. If the displacement made by the body is $(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}) \ma...

A small disc of mass \(m\) slides down with initial velocity zero from the top \((A)\) of a smooth hill of height \(H\) having a horizontal portion \((BC)\) as shown in the figure. If the height of the horizontal portion of the hill is $$h$...

A block of mass 50 kg is pulled with a constant speed of \(4 \mathrm{~ms}^{-1}\) across a horizontal floor by an applied force of 500 N directed \(30^{\circ}\) above the horizontal. The rate at which the force does work on the block in watt...

A mass of 1 kg falls from a height of 1 m and lands on a massless platform supported by a spring having spring constant \(15 \mathrm{~Nm}^{-1}\) as shown in the figure. The maximum compression of the spring is (acceleration due to gravity $...

A bead of mass 400 g is moving along a straight line under a force that delivers a constant power 1.2 W to the bead. If the bead is initially at rest, the speed it attains after 6 s in \(\mathrm{ms}^{-1}\)

A ball of mass 300 g is dropped from a height 10 m above a sandy ground. On reaching the ground, it penetrates through a distance 1.5 m in sand and finally stops. The average resistance offered by the sand to oppose the motion is (accelerat...

A uniform chain has a mass m and length \(l\).
It is held on a frictionless table with
one-sixth of its length hanging over the edge.
The work done in just pulling the hanging
part back on the table is

A rifle bullet loses \(\left(\frac{1}{25}\right)\)th of its velocity in passing through a plank. The least number of such planks required just to stop the bullet is

When a force F = 17 \(-\) 2x + 6x\(^2\)N acts on a body of mass 2 kg and displaces it from x = 0 m to x = 8 m, the work done is

The range of a projectile is 100 m. Its kinetic
energy will be maximum after covering a
distance of

Water is falling on the blades of a turbine from a height of \(25 \mathrm{~m}\) and \(3 \times 10^3 \mathrm{~kg}\) of water pours on the blade per minute. If the whole of energy is transferred to the turbine, then power delivered is

Two bodies having kinetic energy in the ratio
4 : 1, are moving with same linear velocity.
The ratio of their masses is

An engine develops 20 kW of power. How
much time will it take to lift a mass of 200 kg
to a height of 40 m? (g = 10 ms\(^{-2}\)
)

A body of mass 8 kg, under the action of a
force, is displaced according to the equation, \(s=\frac{t^2}{4}\) m, where t is the time. Find the work done by the force in the first 4 s.

A quarter horse power motor runs at a speed
of 600 rpm. Assuming 60% efficiency, the
work done by the motor in one rotation is

What is the shape of the graph between
speed and kinetic energy of a body?